Question 1

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Answer:

Question 1a:
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1a.JPG
question 1a

in my opinion, we need to change it into conjunctive normal form, so, there must be a conjunction in the clauses.
therefore, i'll use negation to make the disjunction into conjunction.

Question 1b:

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It is proved that the inference in first-order logic is valid using resolution.


Question 1c:
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from the above table, we can prove that the inference is valid.

**another answer from my opinion:
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From the above table, it is shown that the inference is valid.


Chieng : He he... come comment your 1 c already, Do u still rem lecture time the example that we have?

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We tried to prove by truth table rite?
But we can't get all T T T T T T T T T T T T at the end.
However, from the truth table, we can c that :
when B Is T, no matter A is what, A V B is T.
But negate B will be F, to let negate B V C to be T, C have to be T.

same case, when negate B is T, no matter C is what, negate B V C is T.
but in this case B is F, to let A V B to be T, A have to be T.
so, we can see that it depend on A and C actually to decide whether it's True or false, so the resolution is A V C.
In question c, it's actually exactly the same. The only different is A, B, C change to P, Q ,R, isn't it? let see the picture below.

1c.png

From the truth table above, we can c that :
when Q Is T, no matter negate P is what, negate P V Q is T.
But negate Q will be F, to let negate Q V R to be T, R have to be T.

same case, when negate Q is T, no matter R is what, negate Q V R is T.
but in this case Q is F, to let negate P V Q to be T, negate P have to be T.
so, we can see that it depend on negate P and R to decide whether it's True or false, so the resolution is negate P V R.

Question 1d:
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Question 2


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Answer:



Wiki-week6-question_2.jpg

p/s:
carol: dear group member, we'll doing ques 1, ok? ^_^
chieng: Each of us please take one question, ok? First come first serve.
Nick choo: Question 2 done by Choo Pei Ching , for question 2b will upload soon
Chieng: Question 2 is extra for us already, 1 group only need do 1 question, but no wrong for do more right? ^ ^ Nick,2d
CNF (conjunctive normal form) I think there is a mistake . Has to use N instead of U. He he ! Change it?
Chieng: Choon see.... why u del my answer? sob sob...
choon see:sory chieng, mis-press the button and i m not realize your answer is deleted d.Sorry lo..+_+
Boon ding: I done question 1.c. can please comment? ^_^


Name:
Carolyne Alphonsus Tommy
Chieng Lung Hei
Ng Boon Ding
Ng Choon See
Choo Pei Ching